Abstract

The book is devoted to mathematical risk theory - an emerging
branch of probability theory with multiple applications to
economics, finance and other areas of human activities, related
to decision-making under uncertainty. Much attention is paid to
measuring risk, that is, quantitative description of preferences
over sets of probability distributions. An axiomatic approach
for nonlinear preferences is being proposed, which is an
extension of that by J. von Neumann and O. Morgenstern.
Portfolio analysis and risk processes are also considered.

The book is intended for a broad range of readers interested
in application of probability theory to social sciences, including
finance, insurance and individual decision-making in general,
and for graduate students studying mathematics and finance.